Given f (x) equals 3X^3 + KX + 16, and x+2 is a factor of f (x), then what is the value of K?

-4

The Problem:

Given f (x) equals 3x^3 + kx + 16, and x+2 is a factor of f (x), then what is the value of k?

Step-by-step explanation:

If x+c is a factor of P then P (-c) = 0.

So we are given x+2 is a factor of f so f (-2) = 0.

This means we have the following equation:

3 (-2) ^3 + k (-2) + 16=0

Let's solve for k:

3 (-8) - 2k+16=0

-24-2k+16=0

-8-2k=0

-8=2k

-4=k

k=-4